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Teor. Veroyatnost. i Primenen., 1976, Volume 21, Issue 1, Pages 128–135 (Mi tvp3280)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

Some remarks on summing independent variables in the non-classical case

V. I. Rotar'

Moscow

Abstract: Let $\{F_{jn}\}_{j=1}^n$ and $\{G_{jn}\}_{j=1}^n$ be two triangular arrays of distribution functions. Let $b_n$ be such that
$$ \sum_{j=1}^nb_n^{-2}\int_0^{b_n}x[1-F_{jn}(x)+F_{jn}(-x)] dx=\delta/n, $$
where $0<\delta\le 1$;
$$ a_{jn}=\int_{-b_n}^{b_n}x dF_{jn}(x),\qquad a'_{jn}=\int_{-b_n}^{b_n}x dG_{jn}(x). $$

The paper deals with conditions under which
$$ *\hskip-4,5mm\prod_{j=1}^nF_{jn}(xb_n+a_{jn})- {*\hskip-4,5mm}\prod_{j=1}^nG_{jn}(xb_n+a'_{jn})\to 0 $$
weakly with respect to the classes $C$ or $C_0$.

Full text: PDF file (440 kB)

English version:
Theory of Probability and its Applications, 1976, 21:1, 130–137

Bibliographic databases:

Received: 31.10.1974

Citation: V. I. Rotar', “Some remarks on summing independent variables in the non-classical case”, Teor. Veroyatnost. i Primenen., 21:1 (1976), 128–135; Theory Probab. Appl., 21:1 (1976), 130–137

Citation in format AMSBIB
\Bibitem{Rot76}
\by V.~I.~Rotar'
\paper Some remarks on summing independent variables in the non-classical case
\jour Teor. Veroyatnost. i Primenen.
\yr 1976
\vol 21
\issue 1
\pages 128--135
\mathnet{http://mi.mathnet.ru/tvp3280}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=402870}
\zmath{https://zbmath.org/?q=an:0368.60064}
\transl
\jour Theory Probab. Appl.
\yr 1976
\vol 21
\issue 1
\pages 130--137
\crossref{https://doi.org/10.1137/1121010}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. I. Rotar', “On summation of independent variables in a non-classical situation”, Russian Math. Surveys, 37:6 (1982), 151–175  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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